= Cardiac index
{title2=$\mathrm{CI}=Q/\mathrm{BSA}$}
\b[Cardiac index] is <cardiac output> divided by <body surface area>:
$$
\mathrm{CI}=\frac{Q}{\mathrm{BSA}}.
$$
When $Q$ is in L/min and area in m$^2$, its units are L/(min m$^2$). Despite the word index, it is not dimensionless. A primary comparison of <thermodilution> and estimated <Fick principle> measurements explicitly indexed output to body surface area for its analyses.<Thermodilution vs Estimated Fick Cardiac Output Measurement in Clinical Practice by Alexander R. Opotowsky and others>[Abstract, Exposures]{ref}
An original comparison shows how normalization can change ranking. Output 5 L/min with area 2 m$^2$ gives 2.5 L/(min m$^2$). Output 4 L/min with area 1.5 m$^2$ gives about 2.67 L/(min m$^2$). The second output is lower in absolute terms but higher after this area normalization. Neither statement contradicts the other.
The denominator is often estimated rather than directly measured. If the <Mosteller formula> is chosen, with numerical height $h_{\rm cm}$ in centimetres and body mass $m_{\rm kg}$ in kilograms, then
$$
\mathrm{CI}=Q\sqrt{\frac{3600}{h_{\rm cm}m_{\rm kg}}}.
$$
The unit-specific area equation is documented in the official VA technical manual.<Formulas for Body Surface Area Calculator in the VA Clinical Reminders Manager's Manual>[Printed p.36]{ref} Choosing an area model is consequently part of defining the reported index.
For small input errors, $\delta\mathrm{CI}/\mathrm{CI}\simeq\delta Q/Q-\delta\mathrm{BSA}/\mathrm{BSA}$. An overestimated area can lower the index without changing the underlying output measurement. Area normalization also does not by itself account for every difference in metabolism or body composition. The quantity is a standardized way of expressing flow relative to one body-size measure, not an additional independent observation of how much <blood> the <heart> pumps.
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